Matematik

hjælp-regression

28. februar 2011 af larsdrengen (Slettet) - Niveau: B-niveau

 <b style="mso-bidi-font-weight: normal"><span lang="EN-US" style="mso-bidi-font-size:10.5pt;mso-bidi-font-family: "Times New Roman";color:black;mso-ansi-language:EN-US">Hvert år opgøres de danske bankers samlede nettogebyrindtægt for 1. halvår, her kaldet DHN. Tabellen viser DHN for hvert af årene i perioden 2002-2006.

<p class="MsoNormal" style="mso-pagination:none;tab-stops:28.0pt 56.0pt 84.0pt 112.0pt 140.0pt 168.0pt 196.0pt 224.0pt 252.0pt 280.0pt 308.0pt 336.0pt; mso-layout-grid-align:none;text-autospace:none"><b style="mso-bidi-font-weight: normal"><span lang="EN-US" style="mso-bidi-font-size:10.5pt;mso-bidi-font-family: "Times New Roman";color:black;mso-ansi-language:EN-US">I en model antages det, at DHN (mia. kr.) som funktion af tiden <b style="mso-bidi-font-weight: normal"><span lang="EN-US" style="mso-bidi-font-size:11.0pt;mso-bidi-font-family: "Times New Roman";color:black;mso-ansi-language:EN-US">x <span lang="EN-US" style="mso-bidi-font-size: 10.5pt;mso-bidi-font-family:"Times New Roman";color:black;mso-ansi-language: EN-US">(antal år efter 2002) med god tilnærmelse kan beskrives ved en eksponentiel udvikling <span lang="EN-US" style="mso-bidi-font-size:11.0pt;mso-bidi-font-family:"Times New Roman"; color:black;mso-ansi-language:EN-US">f<b style="mso-bidi-font-weight: normal"><span lang="EN-US" style="mso-bidi-font-size:10.5pt;mso-bidi-font-family: "Times New Roman";color:black;mso-ansi-language:EN-US">.</o:p> <p class="MsoNormal" style="mso-pagination:none;tab-stops:28.0pt 56.0pt 84.0pt 112.0pt 140.0pt 168.0pt 196.0pt 224.0pt 252.0pt 280.0pt 308.0pt 336.0pt; mso-layout-grid-align:none;text-autospace:none"><b style="mso-bidi-font-weight: normal"><span lang="EN-US" style="mso-bidi-font-size:10.5pt;mso-bidi-font-family: "Times New Roman";color:black;mso-ansi-language:EN-US"> </o:p> <p class="MsoNormal" style="mso-pagination:none;tab-stops:28.0pt 56.0pt 84.0pt 112.0pt 140.0pt 168.0pt 196.0pt 224.0pt 252.0pt 280.0pt 308.0pt 336.0pt; mso-layout-grid-align:none;text-autospace:none"><b style="mso-bidi-font-weight: normal"><span lang="EN-US" style="mso-bidi-font-size:10.5pt;mso-bidi-font-family: "Times New Roman";color:black;mso-ansi-language:EN-US"> </o:p> <p class="MsoNormal" style="mso-pagination:none;tab-stops:28.0pt 56.0pt 84.0pt 112.0pt 140.0pt 168.0pt 196.0pt 224.0pt 252.0pt 280.0pt 308.0pt 336.0pt; mso-layout-grid-align:none;text-autospace:none"><b style="mso-bidi-font-weight: normal"><span lang="EN-US" style="mso-bidi-font-size:10.5pt;mso-bidi-font-family: "Times New Roman";color:black;mso-ansi-language:EN-US"> </o:p> <table class="MsoTableGrid" border="1" cellspacing="0" cellpadding="0" style="border-collapse:collapse;border:none;mso-border-alt:solid black; mso-border-themecolor:text1;mso-border-alt:.5pt;mso-yfti-tbllook:191; mso-padding-alt:0cm 5.4pt 0cm 5.4pt;mso-border-insideh:.5pt solid black; mso-border-insideh-themecolor:text1;mso-border-insidev:.5pt solid black; mso-border-insidev-themecolor:text1"> <td width="81" valign="top" style="width:81.4pt;border:solid black;mso-border-themecolor: text1;border:1.0pt;mso-border-alt:solid black;mso-border-themecolor:text1; mso-border-alt:.5pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="mso-pagination:none;tab-stops:28.0pt 56.0pt 84.0pt 112.0pt 140.0pt 168.0pt 196.0pt 224.0pt 252.0pt 280.0pt 308.0pt 336.0pt; mso-layout-grid-align:none;text-autospace:none"><b style="mso-bidi-font-weight: normal"><span lang="EN-US" style="mso-bidi-font-size:10.5pt;mso-bidi-font-family: "Times New Roman";color:black;mso-ansi-language:EN-US">Årstal</o:p> <p class="MsoNormal" style="mso-pagination:none;tab-stops:28.0pt 56.0pt 84.0pt 112.0pt 140.0pt 168.0pt 196.0pt 224.0pt 252.0pt 280.0pt 308.0pt 336.0pt; mso-layout-grid-align:none;text-autospace:none"><b style="mso-bidi-font-weight: normal"><span lang="EN-US" style="mso-bidi-font-size:10.5pt;mso-bidi-font-family: "Times New Roman";color:black;mso-ansi-language:EN-US"> </o:p> <p class="MsoNormal" style="mso-pagination:none;tab-stops:28.0pt 56.0pt 84.0pt 112.0pt 140.0pt 168.0pt 196.0pt 224.0pt 252.0pt 280.0pt 308.0pt 336.0pt; mso-layout-grid-align:none;text-autospace:none"><b style="mso-bidi-font-weight: normal"><span lang="EN-US" style="mso-bidi-font-size:10.5pt;mso-bidi-font-family: "Times New Roman";color:black;mso-ansi-language:EN-US"> </o:p> <td width="81" valign="top" style="width:81.4pt;border:solid black;mso-border-themecolor: text1;border:1.0pt;border-left:none;mso-border-left-alt:solid black; mso-border-left-themecolor:text1;mso-border-left-alt:.5pt;mso-border-alt: solid black;mso-border-themecolor:text1;mso-border-alt:.5pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="mso-pagination:none;tab-stops:28.0pt 56.0pt 84.0pt 112.0pt 140.0pt 168.0pt 196.0pt 224.0pt 252.0pt 280.0pt 308.0pt 336.0pt; mso-layout-grid-align:none;text-autospace:none"><b style="mso-bidi-font-weight: normal"><span lang="EN-US" style="mso-bidi-font-size:10.5pt;mso-bidi-font-family: "Times New Roman";color:black;mso-ansi-language:EN-US">2002</o:p> <td width="81" valign="top" style="width:81.45pt;border:solid black;mso-border-themecolor: text1;border:1.0pt;border-left:none;mso-border-left-alt:solid black; mso-border-left-themecolor:text1;mso-border-left-alt:.5pt;mso-border-alt: solid black;mso-border-themecolor:text1;mso-border-alt:.5pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="mso-pagination:none;tab-stops:28.0pt 56.0pt 84.0pt 112.0pt 140.0pt 168.0pt 196.0pt 224.0pt 252.0pt 280.0pt 308.0pt 336.0pt; mso-layout-grid-align:none;text-autospace:none"><b style="mso-bidi-font-weight: normal"><span lang="EN-US" style="mso-bidi-font-size:10.5pt;mso-bidi-font-family: "Times New Roman";color:black;mso-ansi-language:EN-US">2003</o:p> <td width="81" valign="top" style="width:81.45pt;border:solid black;mso-border-themecolor: text1;border:1.0pt;border-left:none;mso-border-left-alt:solid black; mso-border-left-themecolor:text1;mso-border-left-alt:.5pt;mso-border-alt: solid black;mso-border-themecolor:text1;mso-border-alt:.5pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="mso-pagination:none;tab-stops:28.0pt 56.0pt 84.0pt 112.0pt 140.0pt 168.0pt 196.0pt 224.0pt 252.0pt 280.0pt 308.0pt 336.0pt; mso-layout-grid-align:none;text-autospace:none"><b style="mso-bidi-font-weight: normal"><span lang="EN-US" style="mso-bidi-font-size:10.5pt;mso-bidi-font-family: "Times New Roman";color:black;mso-ansi-language:EN-US">2004</o:p> <td width="81" valign="top" style="width:81.45pt;border:solid black;mso-border-themecolor: text1;border:1.0pt;border-left:none;mso-border-left-alt:solid black; mso-border-left-themecolor:text1;mso-border-left-alt:.5pt;mso-border-alt: solid black;mso-border-themecolor:text1;mso-border-alt:.5pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="mso-pagination:none;tab-stops:28.0pt 56.0pt 84.0pt 112.0pt 140.0pt 168.0pt 196.0pt 224.0pt 252.0pt 280.0pt 308.0pt 336.0pt; mso-layout-grid-align:none;text-autospace:none"><b style="mso-bidi-font-weight: normal"><span lang="EN-US" style="mso-bidi-font-size:10.5pt;mso-bidi-font-family: "Times New Roman";color:black;mso-ansi-language:EN-US">2005</o:p> <td width="81" valign="top" style="width:81.45pt;border:solid black;mso-border-themecolor: text1;border:1.0pt;border-left:none;mso-border-left-alt:solid black; mso-border-left-themecolor:text1;mso-border-left-alt:.5pt;mso-border-alt: solid black;mso-border-themecolor:text1;mso-border-alt:.5pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="mso-pagination:none;tab-stops:28.0pt 56.0pt 84.0pt 112.0pt 140.0pt 168.0pt 196.0pt 224.0pt 252.0pt 280.0pt 308.0pt 336.0pt; mso-layout-grid-align:none;text-autospace:none"><b style="mso-bidi-font-weight: normal"><span lang="EN-US" style="mso-bidi-font-size:10.5pt;mso-bidi-font-family: "Times New Roman";color:black;mso-ansi-language:EN-US">2006</o:p> <td width="81" valign="top" style="width:81.4pt;border:solid black;mso-border-themecolor: text1;border:1.0pt;border-top:none;mso-border-top-alt:solid black;mso-border-top-themecolor: text1;mso-border-top-alt:.5pt;mso-border-alt:solid black;mso-border-themecolor: text1;mso-border-alt:.5pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="mso-pagination:none;tab-stops:28.0pt 56.0pt 84.0pt 112.0pt 140.0pt 168.0pt 196.0pt 224.0pt 252.0pt 280.0pt 308.0pt 336.0pt; mso-layout-grid-align:none;text-autospace:none"><b style="mso-bidi-font-weight: normal"><span lang="EN-US" style="mso-bidi-font-size:10.5pt;mso-bidi-font-family: "Times New Roman";color:black;mso-ansi-language:EN-US">DHN (mia. Kr.)</o:p> <td width="81" valign="top" style="width:81.4pt;border-top:none;border-left:none; border-bottom:solid black;mso-border-bottom-themecolor:text1;border-bottom: 1.0pt;border-right:solid black;mso-border-right-themecolor:text1;border-right: 1.0pt;mso-border-top-alt:solid black;mso-border-top-themecolor:text1; mso-border-top-alt:.5pt;mso-border-left-alt:solid black;mso-border-left-themecolor: text1;mso-border-left-alt:.5pt;mso-border-alt:solid black;mso-border-themecolor: text1;mso-border-alt:.5pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="mso-pagination:none;tab-stops:28.0pt 56.0pt 84.0pt 112.0pt 140.0pt 168.0pt 196.0pt 224.0pt 252.0pt 280.0pt 308.0pt 336.0pt; mso-layout-grid-align:none;text-autospace:none"><b style="mso-bidi-font-weight: normal"><span lang="EN-US" style="mso-bidi-font-size:10.5pt;mso-bidi-font-family: "Times New Roman";color:black;mso-ansi-language:EN-US">6,697</o:p> <td width="81" valign="top" style="width:81.45pt;border-top:none;border-left: none;border-bottom:solid black;mso-border-bottom-themecolor:text1;border-bottom: 1.0pt;border-right:solid black;mso-border-right-themecolor:text1;border-right: 1.0pt;mso-border-top-alt:solid black;mso-border-top-themecolor:text1; mso-border-top-alt:.5pt;mso-border-left-alt:solid black;mso-border-left-themecolor: text1;mso-border-left-alt:.5pt;mso-border-alt:solid black;mso-border-themecolor: text1;mso-border-alt:.5pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="mso-pagination:none;tab-stops:28.0pt 56.0pt 84.0pt 112.0pt 140.0pt 168.0pt 196.0pt 224.0pt 252.0pt 280.0pt 308.0pt 336.0pt; mso-layout-grid-align:none;text-autospace:none"><b style="mso-bidi-font-weight: normal"><span lang="EN-US" style="mso-bidi-font-size:10.5pt;mso-bidi-font-family: "Times New Roman";color:black;mso-ansi-language:EN-US">7,160</o:p> <td width="81" valign="top" style="width:81.45pt;border-top:none;border-left: none;border-bottom:solid black;mso-border-bottom-themecolor:text1;border-bottom: 1.0pt;border-right:solid black;mso-border-right-themecolor:text1;border-right: 1.0pt;mso-border-top-alt:solid black;mso-border-top-themecolor:text1; mso-border-top-alt:.5pt;mso-border-left-alt:solid black;mso-border-left-themecolor: text1;mso-border-left-alt:.5pt;mso-border-alt:solid black;mso-border-themecolor: text1;mso-border-alt:.5pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="mso-pagination:none;tab-stops:28.0pt 56.0pt 84.0pt 112.0pt 140.0pt 168.0pt 196.0pt 224.0pt 252.0pt 280.0pt 308.0pt 336.0pt; mso-layout-grid-align:none;text-autospace:none"><b style="mso-bidi-font-weight: normal"><span lang="EN-US" style="mso-bidi-font-size:10.5pt;mso-bidi-font-family: "Times New Roman";color:black;mso-ansi-language:EN-US">8,137</o:p> <td width="81" valign="top" style="width:81.45pt;border-top:none;border-left: none;border-bottom:solid black;mso-border-bottom-themecolor:text1;border-bottom: 1.0pt;border-right:solid black;mso-border-right-themecolor:text1;border-right: 1.0pt;mso-border-top-alt:solid black;mso-border-top-themecolor:text1; mso-border-top-alt:.5pt;mso-border-left-alt:solid black;mso-border-left-themecolor: text1;mso-border-left-alt:.5pt;mso-border-alt:solid black;mso-border-themecolor: text1;mso-border-alt:.5pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="mso-pagination:none;tab-stops:28.0pt 56.0pt 84.0pt 112.0pt 140.0pt 168.0pt 196.0pt 224.0pt 252.0pt 280.0pt 308.0pt 336.0pt; mso-layout-grid-align:none;text-autospace:none"><b style="mso-bidi-font-weight: normal"><span lang="EN-US" style="mso-bidi-font-size:10.5pt;mso-bidi-font-family: "Times New Roman";color:black;mso-ansi-language:EN-US">8,408</o:p> <td width="81" valign="top" style="width:81.45pt;border-top:none;border-left: none;border-bottom:solid black;mso-border-bottom-themecolor:text1;border-bottom: 1.0pt;border-right:solid black;mso-border-right-themecolor:text1;border-right: 1.0pt;mso-border-top-alt:solid black;mso-border-top-themecolor:text1; mso-border-top-alt:.5pt;mso-border-left-alt:solid black;mso-border-left-themecolor: text1;mso-border-left-alt:.5pt;mso-border-alt:solid black;mso-border-themecolor: text1;mso-border-alt:.5pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="mso-pagination:none;tab-stops:28.0pt 56.0pt 84.0pt 112.0pt 140.0pt 168.0pt 196.0pt 224.0pt 252.0pt 280.0pt 308.0pt 336.0pt; mso-layout-grid-align:none;text-autospace:none"><b style="mso-bidi-font-weight: normal"><span lang="EN-US" style="mso-bidi-font-size:10.5pt;mso-bidi-font-family: "Times New Roman";color:black;mso-ansi-language:EN-US">10,538</o:p> <p class="MsoNormal" style="mso-pagination:none;tab-stops:28.0pt 56.0pt 84.0pt 112.0pt 140.0pt 168.0pt 196.0pt 224.0pt 252.0pt 280.0pt 308.0pt 336.0pt; mso-layout-grid-align:none;text-autospace:none"><b style="mso-bidi-font-weight: normal"><span lang="EN-US" style="mso-bidi-font-size:10.5pt;mso-bidi-font-family: "Times New Roman";color:black;mso-ansi-language:EN-US"> </o:p> <p class="MsoNormal" style="mso-pagination:none;tab-stops:28.0pt 56.0pt 84.0pt 112.0pt 140.0pt 168.0pt 196.0pt 224.0pt 252.0pt 280.0pt 308.0pt 336.0pt; mso-layout-grid-align:none;text-autospace:none"><b style="mso-bidi-font-weight: normal"><span lang="EN-US" style="mso-bidi-font-size:10.5pt;mso-bidi-font-family: "Times New Roman";color:black;mso-ansi-language:EN-US">(a)</o:p> <p class="MsoNormal" style="mso-pagination:none;tab-stops:28.0pt 56.0pt 84.0pt 112.0pt 140.0pt 168.0pt 196.0pt 224.0pt 252.0pt 280.0pt 308.0pt 336.0pt; mso-layout-grid-align:none;text-autospace:none"><b style="mso-bidi-font-weight: normal"><span lang="EN-US" style="mso-bidi-font-size:10.5pt;mso-bidi-font-family: "Times New Roman";color:black;mso-ansi-language:EN-US">Benyt tabellens data til at bestemme en forskrift for <span lang="EN-US" style="mso-bidi-font-size:11.0pt;mso-bidi-font-family:"Times New Roman"; color:black;mso-ansi-language:EN-US">f<b style="mso-bidi-font-weight: normal"><span lang="EN-US" style="mso-bidi-font-size:10.5pt;mso-bidi-font-family: "Times New Roman";color:black;mso-ansi-language:EN-US">: <p class="MsoNormal" style="mso-pagination:none;tab-stops:28.0pt 56.0pt 84.0pt 112.0pt 140.0pt 168.0pt 196.0pt 224.0pt 252.0pt 280.0pt 308.0pt 336.0pt; mso-layout-grid-align:none;text-autospace:none"> <p class="MsoNormal" style="mso-pagination:none;tab-stops:28.0pt 56.0pt 84.0pt 112.0pt 140.0pt 168.0pt 196.0pt 224.0pt 252.0pt 280.0pt 308.0pt 336.0pt; mso-layout-grid-align:none;text-autospace:none"><b style="mso-bidi-font-weight: normal"><span lang="EN-US" style="mso-bidi-font-size:10.5pt;mso-bidi-font-family: "Times New Roman";color:black;mso-ansi-language:EN-US"> </o:p> <p class="MsoNormal" style="mso-pagination:none;tab-stops:28.0pt 56.0pt 84.0pt 112.0pt 140.0pt 168.0pt 196.0pt 224.0pt 252.0pt 280.0pt 308.0pt 336.0pt; mso-layout-grid-align:none;text-autospace:none"><b style="mso-bidi-font-weight: normal"><span lang="EN-US" style="mso-bidi-font-size:10.5pt;mso-bidi-font-family: "Times New Roman";color:black;mso-ansi-language:EN-US">(b)</o:p> <p class="MsoNormal" style="mso-pagination:none;tab-stops:28.0pt 56.0pt 84.0pt 112.0pt 140.0pt 168.0pt 196.0pt 224.0pt 252.0pt 280.0pt 308.0pt 336.0pt; mso-layout-grid-align:none;text-autospace:none"><b style="mso-bidi-font-weight: normal"><span lang="EN-US" style="mso-bidi-font-size:10.5pt;mso-bidi-font-family: "Times New Roman";color:black;mso-ansi-language:EN-US">Benyt modellen til at bestemme DHN for 2007 og til at bestemme</o:p>

<span lang="EN-US" style="mso-bidi-font-size:10.5pt;mso-bidi-font-family:"Times New Roman"; color:black;mso-ansi-language:EN-US">fordoblingskonstanten for DHN.</o:p>

<p class="MsoNormal" style="mso-pagination:none;tab-stops:28.0pt 56.0pt 84.0pt 112.0pt 140.0pt 168.0pt 196.0pt 224.0pt 252.0pt 280.0pt 308.0pt 336.0pt; mso-layout-grid-align:none;text-autospace:none"><b style="mso-bidi-font-weight: normal"><span lang="EN-US" style="mso-bidi-font-size:10.5pt;mso-bidi-font-family: "Times New Roman";color:black;mso-ansi-language:EN-US"></o:p>

Brugbart svar (2)

Svar #1
28. februar 2011 af Andersen11 (Slettet)

Lav eksponentiel regression på tabellens data og udnyt den fundne forskrift til at beregne DNH for 2007.


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